"Even in my private conversations with him, he didn't tell me about his visit to North Korea," Menendez, a New Jersey Democrat, said in his statement. "Now I don't expect diplomacy to be negotiated out in the open but I do expect for someone who is the nominee to be Secretary of State, when he speaks with committee leadership and is asked specific questions about North Korea, to share some insights about such a visit."

For his part, Cardin said he doesn't believe Pompeo will be an "independent voice in advising the President" and raised concerns about past statements by Pompeo on Muslims and the LGBT community.

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While not unexpected -- both men voted against Pompeo's nomination last year to head the CIA -- their public statements Wednesday further underscore the tough road ahead for Pompeo's quest to become the country's chief diplomat.

It's widely believed that Pompeo will not receive a favorable committee vote, given the Republicans' slim 11-10 majority on the committee and with one Republican, Sen. Rand Paul, already announcing he's a "no."

Still, Pompeo's nomination could be brought to the floor despite an unfavorable vote in the committee. The question then is whether he would get enough votes in the full Senate. With Paul a "no" vote and Sen. John McCain back in Arizona battling cancer, Republicans would need a single Democrat to vote in favor of Pompeo should each of the 49 Republicans vote for the nomination. Should they lose more Republicans, more Democrats would be needed to get the nomination across the finish line.

Pompeo secured support from 15 Democrats and independents when he was nominated for CIA director last year, but it's unclear whether those same senators will back him again. Democratic Sens. Dianne Feinstein of California, Jeanne Shaheen of New Hampshire, and Tim Kaine of Virginia all voted for Pompeo last time but have already expressed opposition to his nomination for secretary of state.

Other Democrats who voted yes last year, like Sen. Joe Manchin of West Virginia and independent Sen. Angus King of Maine, have said they're still considering how they'll vote. Pompeo has been making the rounds on Capitol Hill, meeting with previous "yes" votes, such as Manchin and Democratic Sen. Jack Reed of Rhode Island on Tuesday. On Wednesday, he's set to meet with Democratic Sen. Amy Klobuchar of Minnesota.